Wear prediction method of crane transmission system

Abstract

The invention relates to the technical field of wear prediction, in particular to a wear prediction method of a crane transmission system. Comprising the steps of obtaining tooth profile geometric parameters and material fatigue characteristics, determining a meshing trajectory curve and contact point pressure distribution, obtaining a contact point displacement sequence, extracting trajectory node distribution and calculating curvature distribution, determining a contact point migration rate and velocity gradient distribution, judging a direction angle change rate in the velocity gradient distribution, and determining a velocity abrupt change point coordinate. Calculating the contact point pressure distribution at the mutation point, determining the position of a stress concentration point, calculating the local wear rate, obtaining the local wear distribution data of the tooth surface, carrying out simulation analysis on the stress concentration point distribution of a high-wear area, and recalculating the optimized contact point displacement sequence and local wear distribution data to obtain a contact point distribution optimization result. According to the method, the defects of the traditional technology in wear prediction are overcome, the wear trend can be recognized in the early stage, maintenance and optimization are carried out in advance, and therefore the fault downtime is shortened.

Description

Technical Field

[0001] This invention relates to the field of wear prediction technology, and in particular to a method for predicting wear in a crane transmission system. Background Technology

[0002] Cranes, as heavy machinery, play a vital role in material handling in construction sites, ports, and other locations. Their transmission system, as the core component of the crane, is responsible for transmitting power from the power source to the hook. Due to the long-term operation of cranes under high load and high frequency conditions, wear on the gears in the transmission system gradually becomes a prominent issue, directly affecting the crane's service life and operating efficiency.

[0003] In traditional crane drive systems, gear wear is typically only discovered after equipment malfunctions, leading to high costs for repair and replacement, as well as increased downtime. Therefore, predicting gear wear and implementing effective monitoring and early warning mechanisms for proactive maintenance is a pressing technical challenge in the crane drive system field.

[0004] In existing technologies, most methods rely on traditional monitoring techniques based on vibration analysis, oil monitoring, or temperature monitoring to infer the health status of gears. However, these methods struggle to achieve accurate wear prediction and have poor adaptability to the operating environment and conditions of the equipment. Traditional wear prediction techniques often depend on empirical judgment or simple statistical models, lacking dynamic simulation and comprehensive analysis of the gear meshing process.

[0005] To address this technical challenge, the introduction of modern computer simulation technology and finite element analysis (FEA) methods has provided a new direction for gear wear prediction. By accurately obtaining gear design parameters and combining material properties with finite element analysis, it is possible to more accurately simulate the wear process of gears under actual working conditions, predict high-wear areas, and optimize gear design, thereby effectively improving the reliability and lifespan of the transmission system.

[0006] However, most current finite element analysis methods focus on static or simple dynamic calculations, lacking refined analysis for high-load conditions, especially complex conditions in heavy machinery such as cranes. Therefore, an advanced predictive method that comprehensively considers gear geometry, material properties, and dynamic behavior is needed to provide early warnings of wear trends and optimize the design of crane transmission systems, thereby improving overall efficiency and safety.

[0007] Therefore, this invention provides a wear prediction method for crane transmission systems. By combining gear design, material properties, and finite element analysis, it overcomes the shortcomings of traditional technologies in wear prediction, enabling early identification of wear trends and timely maintenance and optimization, thereby reducing downtime and improving equipment efficiency and economy. Summary of the Invention

[0008] This invention provides a method for predicting wear in a crane transmission system, mainly comprising: Step S1: Obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence; Step S2: Extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; Step S3: Determine the rate of change of the direction angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and calculate the contact pressure distribution at the abrupt change point using Hertzian contact theory; Step S4: Determine the location of stress concentration points based on the contact pressure distribution at the abrupt change point, calculate the local wear rate using the wear rate calculation formula, and obtain local wear distribution data of the tooth surface; Step S5: Based on the local wear distribution data, contact point pressure distribution, and dynamic simulation model, the high wear area is obtained and used as wear prediction data. The stress concentration point distribution in the high wear area is analyzed by dynamic finite element simulation. The curvature radius is adjusted to generate improved tooth profile geometric parameters. The optimized contact point displacement sequence and local wear distribution data are recalculated to obtain the optimized contact point distribution results.

[0009] As a preferred embodiment of the present invention, step S1 includes: The gear profile geometric parameters, including tooth profile angle, module, and tooth width, are obtained from the gear design drawings. The tooth surface fatigue characteristics, including fatigue limit and material hardness, are obtained from the material parameters. The contact point displacement sequence and contact point pressure distribution during meshing are calculated using the finite element analysis method. The spatial expression of the meshing trajectory curve in the tooth surface coordinate system is determined. The meshing trajectory curve represents the motion path of the contact point on the tooth surface.

[0010] As a preferred embodiment of the present invention, step S2, which involves extracting the trajectory node distribution and calculating the curvature distribution based on the contact point displacement sequence, includes: The sliding window algorithm is used to extract the trajectory node distribution from the contact point displacement sequence, calculate the trajectory curvature distribution at each node, and determine the spatial position of the node in the tooth surface coordinate system. The trajectory curvature distribution characterizes the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node.

[0011] As a preferred embodiment of the present invention, step S2, determining the contact point migration rate and velocity gradient distribution, includes: Based on the distribution of trajectory nodes, the contact point migration rate is calculated, which represents the speed at which the contact point moves on the tooth surface. The velocity gradient distribution is calculated, and the velocity vector and direction angle data at each node are obtained. The velocity vector represents the direction and magnitude of the contact point's movement, and the direction angle data represents the angular change of the velocity vector.

[0012] As a preferred embodiment of the present invention, step S3, determining the rate of change of the direction angle in the velocity gradient distribution and determining the coordinates of the velocity abrupt change point, includes: Based on the velocity gradient distribution, the rate of change of the direction angle is calculated, and it is determined whether the rate of change of the direction angle exceeds a preset threshold for abrupt change. If it exceeds the preset threshold for abrupt change, the velocity abrupt change point is determined through differential analysis, and the coordinates and timestamp of the abrupt change point in the tooth surface coordinate system are obtained. The timestamp represents the time when the abrupt change point occurs.

[0013] As a preferred embodiment of the present invention, step S3, calculating the contact pressure distribution at the abrupt change point using Hertzian contact theory, includes: The contact pressure distribution at the abrupt change point is calculated using Hertzian contact theory based on the coordinates of the abrupt change point and the geometric parameters of the tooth profile. This determines the spatial location of the stress concentration point on the tooth surface. The contact pressure distribution characterizes the stress distribution characteristics at the abrupt change point, and the stress concentration point characterizes a local high-stress region on the tooth surface.

[0014] As a preferred embodiment of the present invention, step S4, calculating the local wear rate using the wear rate calculation formula, includes: For stress concentration points, combined with tooth surface fatigue characteristics and contact point migration rate, the local wear rate is calculated using the wear rate calculation formula W=k×P×v, where W represents the wear rate, k represents the material wear coefficient, P represents the contact point pressure distribution, and v represents the contact point migration rate. This obtains local wear distribution data of the tooth surface, which characterizes the spatial distribution of tooth surface wear.

[0015] As a preferred embodiment of the present invention, step S5 involves using dynamic finite element simulation to analyze the stress concentration point distribution in the high-wear region, including: Based on local wear distribution data and contact point pressure distribution, dynamic finite element simulation is used to analyze the spatial distribution law of tooth surface wear, determine the stress concentration point distribution in high wear areas, and the high wear areas represent areas with severe tooth surface wear. The radius of curvature is adjusted to generate improved tooth profile geometric parameters, which are used to optimize meshing performance.

[0016] Secondly, the present invention also provides a wear prediction system for a crane transmission system, for implementing the above-mentioned method, the system comprising: The first acquisition unit is used to obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence. The determining unit is used to extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and to determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; The calculation unit is used to determine the rate of change of the directional angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and calculate the contact pressure distribution at the abrupt change point using Hertzian contact theory. The second acquisition unit is used to determine the location of stress concentration points based on the contact pressure distribution at the abrupt change point, calculate the local wear rate using the wear rate calculation formula, and acquire local wear distribution data of the tooth surface. The optimization unit is used to obtain the high wear area based on the wear distribution data, analyze the stress concentration point distribution of the high wear area through dynamic finite element simulation, adjust the radius of curvature to generate improved tooth profile geometric parameters, recalculate the optimized contact point displacement sequence and local wear distribution data, and obtain the contact point distribution optimization result.

[0017] Thirdly, the present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the above-described method.

[0018] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: This invention provides a wear prediction method for crane transmission systems by combining gear design, material properties, and dynamic finite element simulation analysis. First, the tooth profile geometry parameters and material fatigue characteristics are obtained from the gear design parameters, and the meshing trajectory curve and contact point pressure distribution are determined through finite element analysis. Next, the contact point displacement sequence is extracted using a sliding window algorithm, and the curvature distribution of the trajectory nodes is calculated to determine the migration rate and velocity gradient distribution of the contact points. This allows for the determination of the contact point's motion direction and its changes, particularly at points of rapid velocity change. Hertzian contact theory is used to calculate the contact point pressure distribution, thereby identifying potential stress concentration points. Furthermore, this invention utilizes dynamic finite element simulation to conduct in-depth analysis of high-wear areas, predicting the wear area and corresponding stress distribution. By adjusting the radius of curvature, the tooth profile geometry parameters are optimized, thereby improving the gear's meshing performance. The above process includes calculating the local wear rate, identifying stress concentration points, and generating local wear distribution data. Finally, the optimized tooth profile geometry parameters are used to optimize the contact point distribution. Through the synergy of these technical solutions, not only can the wear resistance of the gear transmission system be improved, but a scientific basis for design optimization can also be provided, reducing the risk of failure caused by wear, extending equipment service life, and improving the crane's working efficiency and economy. Attached Figure Description

[0019] Figure 1 This is a flowchart of a wear prediction method for a crane transmission system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the contact area between two adjacent gears in the crane transmission system of this invention. Figure 3 This is a structural diagram of a wear prediction system for a crane transmission system according to an embodiment of the present invention. Detailed Implementation

[0020] To further understand the content of this invention, a detailed description of the invention is provided in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. It should also be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0021] like Figure 1 This embodiment provides a method for predicting wear in a crane transmission system, including: Step S1: Obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence; Specifically, this includes: obtaining tooth profile geometric parameters from gear design drawings, including tooth profile angle, module, and tooth width; obtaining tooth surface fatigue characteristics from material parameters, including fatigue limit and material hardness; calculating the contact point displacement sequence and contact point pressure distribution during meshing through finite element analysis; determining the spatial expression of the meshing trajectory curve in the tooth surface coordinate system; and the meshing trajectory curve characterizing the motion path of the contact point on the tooth surface.

[0022] Specifically, since gears are the core components of a crane's transmission system, the wear of gears determines the wear of the entire transmission system. Therefore, by obtaining the tooth profile geometric parameters, such as tooth angle, module, and tooth width, from the gear design drawings, these geometric parameters provide preliminary geometric characteristics for calculating the displacement and pressure distribution at the contact points. The tooth angle and module determine the gear's meshing method and contact characteristics, while the tooth width affects the gear's load-bearing capacity and the distribution of its working area. Furthermore, the tooth surface fatigue characteristics, including fatigue limit and material hardness, are obtained from material parameters. The fatigue limit reflects the material's durability under long-term load, while the material hardness affects the tooth surface's ability to resist wear and plastic deformation. A three-dimensional geometric model of the gear pair is established using the finite element method (FEA). The gear tooth profile is discretized into a finite number of nodal elements, each containing position coordinates, material properties, and boundary condition information. Using this method, the relative motion between the driving gear and the driven gear can be simulated during meshing. The driving gear rotates at a constant angular velocity, while the driven gear rotates according to the transmission ratio. The displacement sequence of the contact point on the tooth surface, i.e., the contact point displacement sequence, is obtained by solving the displacement vector within a unit time step. The aforementioned unit time is not long, which can be 2 seconds. The displacement sequence of the contact point includes three components: radial, tangential, and axial displacement, which completely depicts the motion trajectory of the contact point during meshing.

[0023] By measuring the stress tensor of the contact area using sensors, the pressure distribution at the contact point can be further obtained. In the finite element model, Hertzian contact theory is used to calculate the pressure distribution at the contact point, which is usually elliptical. The maximum pressure in the contact area is located at the center of the contact area and gradually decreases outward. The calculation of contact pressure needs to consider the influence of parameters such as the radius of curvature of the tooth surface, the elastic modulus of the material, and Poisson's ratio.

[0024] The spatial representation of the meshing trajectory curve is achieved by establishing a cylindrical coordinate system in the tooth surface coordinate system. The tooth surface coordinate system has the gear shaft center as the origin, the radial direction as the x-axis, the tangential direction as the y-axis, and the axial direction as the z-axis. The radial coordinate of the node reflects its distance from the gear center, the tangential coordinate represents its angular position in the circumferential direction, and the axial coordinate describes its position in the tooth width direction. The meshing trajectory can comprehensively reflect the specific positional changes of the contact point during the working process.

[0025] The above technical solution combines the geometric design of gears with material properties and uses the finite element analysis method to accurately calculate the displacement and pressure at the contact points. This enables wear analysis and optimization of gears under high load and high frequency of use, thereby further improving the service life of gears and the reliability of the transmission system.

[0026] Step S2: Extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; In step S2, the trajectory node distribution is extracted and the curvature distribution is calculated based on the contact point displacement sequence. This includes: extracting the trajectory node distribution from the contact point displacement sequence using a sliding window algorithm, calculating the trajectory curvature distribution at each node, and determining the spatial position of the node in the tooth surface coordinate system. The trajectory curvature distribution characterizes the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node.

[0027] Specifically, to obtain the trajectory changes and curvature distribution during gear meshing, a sliding window algorithm is first used to extract the trajectory node distribution from the contact point displacement sequence. The length of the window is set according to the gear meshing cycle and sampling frequency. The window length can be one-tenth of the meshing cycle, i.e., the time it takes for the gear to rotate one revolution. Each window contains multiple displacement data. The displacement data is linearly fitted to calculate the slope and intercept parameters of the fitted line. When the slope change of adjacent windows exceeds a preset threshold, the position is marked as a trajectory node. The displacement data within the window is preprocessed to remove high-frequency noise, ensuring the smoothness of the data. The preprocessed displacement data is then normalized so that the coordinates of the displacement data are mapped to a standard numerical range. Next, cubic spline interpolation is used to make the discrete displacement points continuous, generating smooth trajectory curve segments. The first and second derivatives of these curve segments provide information on the tangent direction and curvature change of the trajectory.

[0028] When calculating the curvature distribution, a local coordinate system is established at the nodes. A two-dimensional local coordinate system is established with the node position as the origin, the trajectory tangent direction as the positive x-axis, and the direction perpendicular to the tangent as the positive y-axis. Transforming the coordinates of trajectory points within the node's neighborhood into the local coordinate system facilitates curvature calculation and geometric analysis. The establishment of the local coordinate system eliminates the influence of rotation and translation of the global coordinate system, improving the accuracy and stability of curvature calculation. The curvature value can be obtained by calculating the rate of change of the angle between the tangent vectors at the trajectory nodes. A circular arc fitting method is then used to further calculate the node curvature. These curvature values ​​describe the geometric changes of the meshing trajectory curve, characterize the local changes of the tooth surface during meshing, and smooth the curvature distribution to analyze the patterns of curvature changes during meshing. This helps identify areas of concentrated curvature and areas of drastic curvature changes, which are the areas most likely to experience severe wear. Finally, the local coordinates of the node are transformed into three-dimensional coordinates in the tooth surface coordinate system using a coordinate transformation matrix. The coordinate transformation considers the gear's geometric parameters, including basic parameters such as module, pressure angle, helix angle, and number of teeth. The three-dimensional coordinates of the node include radial, tangential, and axial coordinates, comprehensively describing the spatial position of the node on the tooth surface. This technical solution accurately describes the trajectory changes and curvature distribution during gear meshing, providing reliable data support for predicting gear wear in crane transmission systems.

[0029] Further, in step S2, determining the contact point migration rate and velocity gradient distribution includes: Based on the distribution of trajectory nodes, the contact point migration rate is calculated, which represents the speed at which the contact point moves on the tooth surface. The velocity gradient distribution is calculated, and the velocity vector and direction angle data at each node are obtained. The velocity vector represents the direction and magnitude of the contact point's movement, and the direction angle data represents the angular change of the velocity vector.

[0030] Specifically, based on the distribution of trajectory nodes, the contact point migration rate is calculated. The contact point migration rate is used to characterize the movement speed of the contact point on the tooth surface, and includes: Based on the spatial coordinate differences between adjacent nodes in the trajectory node distribution, the displacement vector between nodes is calculated. By extracting the three-dimensional coordinate data of each trajectory node from the tooth surface coordinate system, vector operations are used to determine the displacement components between adjacent nodes. The displacement vector includes components in the radial, tangential, and axial directions. The three-dimensional coordinate data of each trajectory node is extracted through vector operations to ensure the accuracy of the position calculation and reflect the actual movement path of the contact point on the tooth surface. By combining the time interval data during the meshing process, the instantaneous migration rate at each node is calculated by the ratio of the displacement vector to the time interval. The time interval data comes from the discretization of the gear meshing cycle, which divides the continuous meshing process into several time steps. The instantaneous migration rate reflects the speed at which the contact point moves at a specific moment, providing data support for subsequent stress analysis and wear prediction. A weighted average method is used to smooth the instantaneous migration rates of adjacent nodes to eliminate abrupt noise in numerical calculations. The weighting coefficients are determined based on the distance between nodes and the contact pressure distribution. Nodes that are closer and have similar pressure have higher weights. The smoothed migration rate data has better continuity.

[0031] Based on the calculated migration rate, the velocity gradient distribution at the contact point is further calculated, including obtaining the velocity vector and orientation angle data at each node. The specific process is as follows: Based on the migration rate data at each node, the spatial distribution of the velocity gradient is calculated using the finite difference method. The finite difference method obtains the rate of change of velocity in each direction in space by performing difference operations on the velocity values ​​between adjacent nodes. The velocity gradient includes three components: radial gradient, tangential gradient, and normal gradient (i.e., axial gradient), which respectively characterize the velocity variation characteristics in different directions on the tooth surface. The radial gradient reflects the velocity variation along the direction from the tooth root to the tooth tip, the tangential gradient reflects the velocity variation along the tooth profile curve, and the normal gradient reflects the velocity variation perpendicular to the tooth surface. Based on the magnitude and direction of the migration rate, a velocity vector is constructed at each node. The magnitude of the velocity vector is equal to the value of the migration rate, and the vector direction is determined by the movement direction of the contact point. The velocity vector is expressed as a component in the tooth surface coordinate system through vector decomposition to facilitate subsequent numerical calculations and analysis. The angle between the velocity vector and the reference direction of the tooth surface coordinate system is calculated to obtain the direction angle data at each node. The reference direction is usually selected as the tangent direction or radial direction of the tooth profile. The direction angle data is expressed in radians and the value range is from 0 to 2π. The spatial distribution of the direction angle can identify the change pattern and abnormal area of ​​the contact point motion direction. The gradient operator performs spatial differentiation on the orientation angle data to calculate the rate of change distribution of the orientation angle. The gradient operator includes partial differential operations to calculate the rate of change of the orientation angle in each direction of the tooth surface coordinate system. The rate of change of the orientation angle reflects the stability of the contact point's motion direction. Regions with a large rate of change indicate that the contact point's motion direction has changed drastically, which may pose a risk of stress concentration or accelerated wear.

[0032] The above-mentioned technical solution can accurately calculate the migration rate and velocity gradient distribution of gear contact points, providing important basic data for predicting gear wear in crane transmission systems. This method can effectively identify abrupt changes in the motion of contact points, help predict areas of concentrated wear, and thus provide a scientific basis for optimizing gear design, thereby extending the service life of gears and improving the reliability and stability of crane transmission systems.

[0033] Step S3: Determine the rate of change of the direction angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and use Hertz contact theory to calculate the pressure distribution at the contact point at the abrupt change point; In step S3, determining the rate of change of the direction angle in the velocity gradient distribution and determining the coordinates of the velocity abrupt change point includes: Based on the velocity gradient distribution, the rate of change of the direction angle is calculated, and it is determined whether the rate of change of the direction angle exceeds a preset threshold for abrupt change. If it exceeds the preset threshold for abrupt change, the velocity abrupt change point is determined through differential analysis, and the coordinates and timestamp of the abrupt change point in the tooth surface coordinate system are obtained. The timestamp represents the time when the abrupt change point occurs.

[0034] Specifically, based on the velocity gradient distribution, the rate of change of the direction angle at each trajectory node is first calculated. Based on the migration rate and velocity gradient distribution at the contact point, the velocity vector direction angle data at each node is extracted, and the direction angle difference between adjacent nodes is calculated. The rate of change of the direction angle is then solved using the finite difference method, with the specific formula as follows:

[0035] in, Indicates the first The orientation angle of each node For the corresponding time parameters, in actual implementation, if the distribution density of trajectory nodes is high, a three-point difference format is used to improve the calculation accuracy. For boundary nodes, the rate of change of their orientation angle can be processed by weighted average. The calculated rate of change of the orientation angle at each node is compared with a preset threshold for abrupt change. The preset threshold for abrupt change is set based on the gear meshing characteristics and tooth surface fatigue characteristics, for example, the set range is 0.5 rad / ms to 2.0 rad / ms. In this embodiment, for gears with different gear modules and pressure angles, the threshold for abrupt change is set in segments, for example, the threshold for small module gears is 0.8 rad / ms, and the threshold for large module gears is 1.2 rad / ms. When the absolute value of the rate of change of the orientation angle at a certain node exceeds the preset threshold, the node is marked as a potential abrupt change. For the marked potential mutation points, second-order difference analysis is performed to determine their precise locations. The rate of change of the orientation angle is calculated using a central difference scheme, as follows:

[0036] When the sign of the second derivative changes and the magnitude exceeds the preset second-order threshold, the point is confirmed as a real velocity jump point. Typically, the second-order threshold is set to 5.0 radians per millisecond squared to ensure accurate identification of velocity jump phenomena during meshing. The precise coordinates of the mutation point in the tooth surface coordinate system are calculated by interpolation. The cubic spline interpolation algorithm is used to calculate the x, y, and z coordinates of the mutation point based on the coordinate data of the two nodes before and after the mutation point. In the implementation, when the mutation point is located between two trajectory nodes, the Lagrange interpolation polynomial can be used for accurate calculation.

[0037] The tooth surface coordinate system is established with the gear shaft center as the origin, the radial direction as the x-axis, the tangential direction as the y-axis, and the axial direction as the z-axis to ensure the accurate expression of the coordinates of the abrupt change point.

[0038] The timestamp represents the moment when the abrupt change occurs. The precise moment of the abrupt change within the meshing cycle is calculated using a linear interpolation method, as shown in the following formula:

[0039] Here, λ is the interpolation ratio determined by the relative position of the abrupt change point coordinates between the two nodes. and The time parameters are the two nodes before and after the mutation point, respectively. Preferably, the accuracy of the timestamp can be set to 0.01 milliseconds to meet the time resolution requirements of gear dynamic meshing analysis. In a preferred embodiment, for the helical gear meshing process, since the contact line gradually moves along the tooth width direction, the identification of the velocity mutation point needs to consider the influence of the helix angle. When calculating the direction angle change rate, a helix angle correction coefficient is introduced, which is cos(β), where β is the helix angle. For example, for a helical gear with a helix angle of 30 degrees, the correction coefficient is 0.866. The mutation point threshold is adjusted accordingly to 1.15 times the original value to ensure the accuracy of mutation point identification.

[0040] The above technical solution can accurately identify the speed change points of the contact points during gear meshing, providing key data for wear prediction in crane transmission systems. It can also effectively identify changes in the movement direction of the contact points and provide precise location and time information of the change points, thereby providing a scientific basis for gear design optimization, wear analysis and life prediction, and improving the reliability and durability of crane transmission systems.

[0041] Further, in step S3, the pressure distribution at the abrupt change point is calculated using Hertzian contact theory, including: Based on the coordinates of the abrupt change point and the geometric parameters of the tooth profile, the pressure distribution at the contact point at the abrupt change point is calculated using Hertzian contact theory to determine the spatial location of the stress concentration point on the tooth surface. The pressure distribution at the contact point characterizes the stress distribution characteristics at the abrupt change point, and the stress concentration point characterizes a local high-stress region on the tooth surface.

[0042] Specifically, a contact geometry model is established based on the coordinate data of the abrupt change point and the tooth profile geometric parameters. By extracting the spatial position of the abrupt change point in the tooth surface coordinate system and combining it with the tooth surface curvature radius, contact angle, and normal vector data from the tooth profile geometric parameters, a local contact geometry model at the abrupt change point is constructed. This geometry model includes: The principal curvature radii R1 and R2 are the principal curvature radii of the driving gear and the driven gear at the abrupt change point, respectively, which are the local curvature radii of the tooth surfaces of the driving gear and the driven gear.

[0043] relative radius of curvature It is calculated using the formula:

[0044] It is also necessary to determine the direction of the major axis and the minor axis of the contact ellipse at the contact point. These geometric parameters will provide the basic data for Hertzian contact pressure calculation.

[0045] Based on Hertzian contact theory, such as Figure 2As shown, the contact area is assumed to be elliptical, and the contact pressure is distributed ellipsoidally within the elliptical region. Based on the relative radius of curvature and the material's elastic modulus in the contact geometry model, the semi-major axis *a* and semi-minor axis *b* of the contact ellipse are calculated. Their geometric dimensions are obtained through elliptic integral functions, as shown in the following formula:

[0046] Where F is the contact load, E is the equivalent elastic modulus, ν is Poisson's ratio, m and n are preset parameters of the ellipse, and the pressure distribution function at any point in the contact area is:

[0047] Where p0 is the maximum contact pressure, the origin is the center of the ellipse of the contact area, and the lines containing the major and minor axes are the coordinate axes, where x and y are the coordinates inside the contact ellipse. m reflects the elastic properties of the contact ellipse in the direction of the major axis, and n reflects the elastic properties of the contact ellipse in the direction of the minor axis. Both m and n are related to the elastic modulus of the contact surface.

[0048] According to Hertzian contact theory, the maximum contact pressure p0 is located at the center of the contact ellipse, and its value is:

[0049] The maximum contact pressure p0 characterizes the contact intensity at the point of abrupt change. The pressure gradient distribution is obtained by calculating the spatial partial derivative of the pressure distribution function. The specific calculation formula is as follows:

[0050] The magnitude of the pressure gradient is:

[0051] Among them, the areas with larger pressure gradients correspond to locations where stress concentration is more pronounced.

[0052] The stress concentration point is located in the contact pressure distribution where the pressure gradient magnitude exceeds the preset stress concentration threshold. In the region, by traversing all grid points within the contact ellipse, the pressure gradient magnitude of each point is calculated. When the pressure gradient magnitude |▽p| of a point is greater than a set threshold, the point is marked as a candidate point for stress concentration. After cluster analysis, all candidate points are grouped into the same stress concentration region if the spatial distance is less than the cluster radius. The geometric center of each region is taken as the stress concentration point of that region. The above technical solution enables accurate calculation of the contact pressure distribution at the abrupt change point during gear meshing, and identifies the location of stress concentration points through pressure gradient analysis. This method can not only accurately assess the contact pressure and stress distribution during gear meshing, but also provide a scientific basis for further wear prediction, tooth profile optimization, and gear design of crane transmission systems.

[0053] Step S4: Determine the location of stress concentration points, calculate the local wear rate using the wear rate calculation formula, and obtain local wear distribution data of the tooth surface; In step S4, the local wear rate is calculated using the wear rate calculation formula, including: Based on stress concentration points, combined with tooth surface fatigue characteristics and contact point migration rate, the local wear rate is calculated using the wear rate calculation formula W=k×P×v, where W represents the wear rate, k represents the material wear coefficient, P represents the contact point pressure distribution, and v represents the contact point migration rate. This yields local wear distribution data of the tooth surface, which characterizes the spatial distribution of tooth surface wear.

[0054] Specifically, based on the coordinates of the stress concentration points and the geometric parameters of the tooth surface, the precise location of the stress concentration points on the tooth surface is determined. Specifically, the spatial location of the stress concentration points is ensured by transforming the coordinates from the elliptical coordinate system corresponding to the contact area to the coordinates within the tooth surface coordinate system. Based on these stress concentration points, the fundamental mechanical property parameters of the gear material, including elastic modulus, Poisson's ratio, yield strength, and fatigue limit, are extracted. Combined with material fatigue test data, a stress-life (SN) curve is fitted. The horizontal and vertical axes represent the magnitude of the stress applied to the material and the fatigue life, i.e., the number of cycles the material can withstand at the corresponding stress magnitude, respectively. This SN curve, i.e., the stress-life curve, can determine the fatigue life characteristics of the material under different stress levels. A fatigue damage accumulation function is established to describe the fatigue damage evolution law of the tooth surface material under cyclic loading. Furthermore, fatigue characteristic parameters are combined with tooth surface hardness distribution, surface roughness, and residual stress distribution to construct a spatial distribution function of tooth surface fatigue characteristics.

[0055] Based on the meshing trajectory curve and trajectory node distribution, the instantaneous velocity vector at each trajectory node is calculated using a numerical differentiation method. The velocity vector is decomposed into tangential and normal components, where the tangential component represents the sliding rate of the contact point along the tooth surface, and the normal component represents the approach and separation rates of the contact point. Combined with gear speed and transmission ratio parameters, the temporal variation law of the contact point migration rate within the meshing cycle is calculated. An interpolation algorithm is then used to extend the discrete velocity data to the entire tooth surface region, forming a continuous distribution field of the contact point migration rate.

[0056] The spatiotemporal distribution characteristics of the contact point migration rate are calculated. Based on the meshing trajectory curve and the distribution of trajectory nodes, the instantaneous velocity vector at each trajectory node is calculated using a numerical differentiation method. The velocity vector is decomposed into tangential and normal components, where the tangential component represents the sliding rate of the contact point along the tooth surface, and the normal component represents the approach and separation rates of the contact point. Combining the gear speed and transmission ratio parameters, the temporal variation law of the contact point migration rate within the meshing cycle is calculated. An interpolation algorithm is used to extend the discrete rate data to the entire tooth surface region, forming a continuous distribution field of the contact point migration rate.

[0057] The wear rate is calculated using the wear rate calculation formula. The material wear coefficient k, the contact point pressure distribution P, and the contact point migration rate v are substituted into the wear rate calculation formula W = k × P × v. The local wear rate values ​​at each location on the tooth surface are obtained through point-by-point calculation.

[0058] A data structure for local wear distribution on the tooth surface is constructed. The calculated local wear rate values ​​are arranged according to the tooth surface coordinates to form a wear rate distribution matrix. The row index of this matrix corresponds to the position in the tooth width direction, the column index corresponds to the position in the tooth height direction, and the matrix element values ​​are the wear rate values ​​at the corresponding positions. The wear rate distribution matrix is ​​visualized using contour plotting to identify the spatial distribution characteristics of high-wear and low-wear areas. Statistical characteristic parameters of the wear distribution data are established, including average wear rate, wear rate standard deviation, and wear concentration index, to quantify the spatial distribution pattern of tooth surface wear.

[0059] For example, in one embodiment, for the wear rate calculation of spur gears, stress concentration points are mainly distributed in the root transition fillet region and the tooth surface region near the pitch line. The root transition fillet region has a high stress concentration coefficient due to the abrupt change in geometry; the contact pressure in this region can reach 2.3 times the average contact pressure. Near the pitch line, the contact point migration rate is relatively low, resulting in a significant sliding friction effect and an increased contribution of the velocity term in the wear rate calculation. Comparative analysis reveals that wear in the root region is mainly dominated by high contact pressure, while wear in the pitch line region is determined by the coupling effect of contact point migration rate and pressure.

[0060] In another possible implementation, the wear distribution of helical gears exhibits a spiral characteristic, which is closely related to the helix angle and the inclination distribution of the contact line. For a helical gear with a helix angle of 30 degrees, the migration rate of the contact point shows a significant gradient distribution along the tooth width, with the migration rate at both ends of the tooth width being about 15% higher than that in the middle. This non-uniformity in rate distribution leads to a trend of tooth surface wear increasing from the middle to both ends of the tooth width. Combined with the spatial variation of tooth surface fatigue characteristics, the local wear distribution data of helical gears shows a complex three-dimensional spatial distribution pattern, requiring the use of three-dimensional interpolation algorithms for data processing and analysis.

[0061] In wear rate calculation, the dynamic influence of tooth surface fatigue characteristics and wear coefficient is combined. After the tooth surface material undergoes a certain number of cyclic loads, the surface microstructure changes, causing the material wear coefficient to exhibit time-varying characteristics. When fatigue damage accumulates to a certain extent, the wear coefficient can increase to 1.8 times the initial value, thus affecting the calculation results of local wear rate.

[0062] The spatial distribution characteristics of localized wear data reflect the spatial pattern of energy dissipation during gear meshing. High-wear areas correspond to locations with high energy dissipation density, and these areas are often the starting points of gear failure. By analyzing the spatial gradient and concentration characteristics of wear distribution, weak points in gear design can be identified, providing a quantitative basis for tooth profile modification and material optimization. Wear distribution data can also be correlated with gear vibration characteristics and noise levels to achieve synergistic optimization of overall gear performance.

[0063] Step S5: Use dynamic finite element simulation to analyze the stress concentration point distribution in the high wear area, adjust the radius of curvature to generate improved tooth profile geometric parameters, recalculate the optimized contact point displacement sequence and local wear distribution data, and obtain the optimized contact point distribution results.

[0064] In step S5, dynamic finite element simulation is used to analyze the stress concentration point distribution in the high-wear area, including: Based on local wear distribution data and contact point pressure distribution, a dynamic simulation model is created. Based on the dynamic simulation model, the spatial distribution law of tooth surface wear is analyzed by dynamic finite element simulation to determine the high wear area and the corresponding stress concentration point distribution. The high wear area represents the area with severe tooth surface wear. The radius of curvature is adjusted to generate improved tooth profile geometric parameters, which are used to optimize meshing performance.

[0065] Specifically, the implementation of the above technical solution includes the following steps: (1) Establish a dynamic simulation model of tooth surface wear, input local wear distribution data as boundary conditions into the finite element mesh nodes, and map the contact point pressure distribution onto the corresponding tooth surface mesh element; the dynamic finite element simulation model uses the Lagrangian description method to establish the tooth surface geometric model, and the tooth surface is meshed, and the mesh density is locally refined in the expected high wear area to improve the calculation accuracy of the area. The simulation model considers the elastic-plastic deformation characteristics of the material and uses a bilinear kinematic hardening model to describe the stress-strain relationship of the material under cyclic load.

[0066] (2) Set dynamic load boundary conditions. Based on the time-varying characteristics of the gear meshing process, the pressure distribution at the contact point is discretized according to the meshing cycle. The magnitude and direction of the load in each time step are determined according to the pressure distribution at the contact point and the meshing position. The load is applied in the form of nodal force. At the same time, tooth root constraint conditions are set to restrict the displacement degrees of freedom of the tooth root node in the radial and tangential directions, so as to maintain the overall stiffness characteristics of the gear.

[0067] (3) Perform dynamic finite element analysis and use the Newmark time integration method to solve the dynamic response of the tooth surface under cyclic load. During the solution process, monitor the stress state of each mesh node, paying particular attention to the distribution of principal stress, shear stress and equivalent stress. The stress tensor of each point on the tooth surface at different times is obtained by calculation, forming the spatiotemporal distribution data of the tooth surface stress field.

[0068] (4) Based on stress field distribution data and local wear distribution data, the spatial distribution pattern of tooth surface wear was identified. Through comparative analysis, it was found that areas with severe wear usually correspond to locations with high stress concentration coefficients, and the stress gradient changes more drastically in these areas. The spatial distribution pattern of wear is characterized by non-uniform distribution along the tooth height direction, especially near the pitch circle and in the transition area between the tooth tip and tooth root, where the degree of wear is relatively high.

[0069] (5) Determine the criteria for high wear areas. Areas with a local wear rate exceeding 1.5 times the average wear rate are defined as high wear areas, i.e., based on predicted wear data. High wear areas are usually distributed near the peak point of tooth surface contact stress and in locations with large changes in contact trajectory curvature. These areas are characterized by obvious stress concentration, rapid accumulation of material fatigue damage, and severe wear.

[0070] (6) Identify stress concentration points in high-wear areas. The spatial coordinates of local stress peak points are determined using stress gradient analysis. Stress concentration point identification is based on equivalent stress distribution; nodes with equivalent stress values ​​exceeding 0.8 times the material's yield strength are selected as potential stress concentration points. By calculating the stress concentration factor of each node, nodes with a stress concentration factor greater than 2.0 are identified as critical stress concentration points, and their position information in the tooth surface coordinate system is recorded.

[0071] Furthermore, by combining the stress concentration point distribution in the high-wear region with the velocity gradient distribution, the radius of curvature is adjusted to generate improved tooth profile geometry parameters. These improved parameters are used to optimize meshing performance. Specifically, this includes: (1) Analyze the relationship between stress concentration points and tooth profile curvature radius. Through geometric analysis, it was found that stress concentration points usually appear at locations with smaller tooth profile curvature radii. The size of the curvature radius directly affects the distribution of contact stress; the smaller the curvature radius, the greater the contact stress, and the easier it is to form stress concentration phenomena.

[0072] (2) Determine the curvature radius adjustment strategy based on the velocity gradient distribution. In regions where the velocity gradient changes drastically, appropriately increase the curvature radius to reduce the peak contact stress. The calculation of the curvature radius adjustment is based on Hertzian contact theory, and a reasonable curvature radius value is determined by controlling the maximum contact stress to not exceed the allowable stress of the material.

[0073] (3) Generate improved tooth profile geometry parameters. This includes key geometric dimensions such as the corrected tooth profile curve equation, addendum circle radius, dedendum circle radius, and transition arc radius. The improved tooth profile geometry parameters optimize the contact stress distribution and reduce stress concentration while maintaining the gear transmission ratio.

[0074] The above technical solution uses the dynamic simulation model and dynamic finite element algorithm to simulate and analyze high-wear areas, wear prediction data, and corresponding stress concentration point distributions. Based on the stress concentration points and velocity gradient distribution, the tooth profile curvature radius is adjusted to generate improved tooth profile geometric parameters. These optimized tooth profile geometric parameters effectively optimize gear meshing performance, improve gear wear resistance, and extend gear service life. Furthermore, based on the identification of high-wear areas, wear distribution can be accurately predicted, providing a basis for gear design and material optimization.

[0075] The present invention also provides a wear prediction system for a crane transmission system, used to implement the above-mentioned method, such as... Figure 3 As shown, the system includes: The first acquisition unit is used to obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence. The determining unit is used to extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and to determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; The calculation unit is used to determine the rate of change of the directional angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and calculate the contact pressure distribution at the abrupt change point using Hertzian contact theory. The second acquisition unit is used to determine the location of stress concentration points based on the contact pressure distribution at the abrupt change point, calculate the local wear rate using the wear rate calculation formula, and acquire local wear distribution data of the tooth surface. The optimization unit is used to obtain the high wear area based on the wear distribution data, analyze the stress concentration point distribution of the high wear area through dynamic finite element simulation, adjust the radius of curvature to generate improved tooth profile geometric parameters, recalculate the optimized contact point displacement sequence and local wear distribution data, and obtain the contact point distribution optimization result.

[0076] The present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the above-described method.

[0077] In summary, this invention provides a wear prediction method for crane transmission systems by combining gear design, material properties, and dynamic finite element simulation analysis. First, the gear profile geometry parameters and material fatigue characteristics are obtained from the gear design parameters, and then the meshing trajectory curve and contact point pressure distribution are determined through finite element analysis. Next, the sliding window algorithm is used to extract the displacement sequence of the contact points and calculate the curvature distribution of the trajectory nodes. This allows for the determination of the migration rate and velocity gradient distribution of the contact points, enabling the identification of the motion direction and its changes at the contact points. In particular, at points of rapid velocity change, the pressure distribution at the contact points is calculated using Hertzian contact theory, thereby identifying possible stress concentration points. Furthermore, this invention utilizes dynamic finite element simulation to conduct in-depth analysis of high-wear areas, predicting the wear areas and corresponding stress distributions. By adjusting the radius of curvature, the tooth profile geometry parameters are optimized, thereby improving the meshing performance of the gears. The above process includes calculating the local wear rate, identifying stress concentration points, and generating local wear distribution data. Finally, the optimized tooth profile geometry parameters are used to optimize the contact point distribution. Through the synergy of these technical solutions, not only can the wear resistance of the gear transmission system be improved, but a scientific basis for design optimization can also be provided, reducing the risk of failure caused by wear, extending equipment service life, and improving the working efficiency and economy of cranes.

[0078] Obviously, those skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. Therefore, if these modifications and variations to the embodiments of this application fall within the scope of the claims of this application and their equivalents, this application also intends to include these modifications and variations.

Claims

1. A method for predicting wear in a crane transmission system, characterized in that, include: Step S1: Obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence; Step S2: Extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; Step S3: Determine the rate of change of the direction angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and calculate the contact pressure distribution at the abrupt change point using Hertzian contact theory; Step S4: Determine the location of stress concentration points based on the contact pressure distribution at the abrupt change point, calculate the local wear rate using the wear rate calculation formula, and obtain local wear distribution data of the tooth surface; Step S5: Based on the local wear distribution data, contact point pressure distribution, and dynamic simulation model, the high wear area is obtained and used as wear prediction data. The stress concentration point distribution in the high wear area is analyzed by dynamic finite element simulation. The curvature radius is adjusted to generate improved tooth profile geometric parameters. The optimized contact point displacement sequence and local wear distribution data are recalculated to obtain the optimized contact point distribution results.

2. The method as described in claim 1, characterized in that, Step S1 includes: The gear profile geometric parameters, including tooth profile angle, module, and tooth width, are obtained from the gear design drawings. The tooth surface fatigue characteristics, including fatigue limit and material hardness, are obtained from the material parameters. The contact point displacement sequence and contact point pressure distribution during meshing are calculated using the finite element analysis method. The spatial expression of the meshing trajectory curve in the tooth surface coordinate system is determined. The meshing trajectory curve represents the motion path of the contact point on the tooth surface.

3. The method as described in claim 1, characterized in that, In step S2, the trajectory node distribution is extracted and the curvature distribution is calculated based on the contact point displacement sequence, including: The sliding window algorithm is used to extract the trajectory node distribution from the contact point displacement sequence, calculate the trajectory curvature distribution at each node, and determine the spatial position of the node in the tooth surface coordinate system. The trajectory curvature distribution characterizes the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node.

4. The method as described in claim 3, characterized in that, In step S2, determining the contact point migration rate and velocity gradient distribution includes: Based on the distribution of trajectory nodes, the contact point migration rate is calculated, which represents the speed at which the contact point moves on the tooth surface. The velocity gradient distribution is calculated, and the velocity vector and direction angle data at each node are obtained. The velocity vector represents the direction and magnitude of the contact point's movement, and the direction angle data represents the angular change of the velocity vector.

5. The method as described in claim 1, characterized in that, In step S3, the rate of change of the direction angle in the velocity gradient distribution is determined, and the coordinates of the velocity abrupt change point are determined, including: Based on the velocity gradient distribution, the rate of change of the direction angle is calculated, and it is determined whether the rate of change of the direction angle exceeds a preset threshold for abrupt change. If it exceeds the preset threshold for abrupt change, the velocity abrupt change point is determined through differential analysis, and the coordinates and timestamp of the abrupt change point in the tooth surface coordinate system are obtained. The timestamp represents the time when the abrupt change point occurs.

6. The method as described in claim 5, characterized in that, In step S3, the pressure distribution at the abrupt change point is calculated using Hertzian contact theory, including: The contact pressure distribution at the abrupt change point is calculated using Hertzian contact theory based on the coordinates of the abrupt change point and the geometric parameters of the tooth profile. This determines the spatial location of the stress concentration point on the tooth surface. The contact pressure distribution characterizes the stress distribution characteristics at the abrupt change point, and the stress concentration point characterizes a local high-stress region on the tooth surface.

7. The method as described in claim 1, characterized in that, In step S4, the local wear rate is calculated using the wear rate calculation formula, including: For stress concentration points, combined with tooth surface fatigue characteristics and contact point migration rate, the local wear rate is calculated using the wear rate calculation formula W=k×P×v, where W represents the wear rate, k represents the material wear coefficient, P represents the contact point pressure distribution, and v represents the contact point migration rate. This obtains local wear distribution data of the tooth surface, which characterizes the spatial distribution of tooth surface wear.

8. The method as described in claim 1, characterized in that, In step S5, dynamic finite element simulation is used to analyze the stress concentration point distribution in the high-wear area, including: Based on local wear distribution data and contact point pressure distribution, dynamic finite element simulation is used to analyze the spatial distribution law of tooth surface wear, determine the stress concentration point distribution in high wear areas, and the high wear areas represent areas with severe tooth surface wear. The radius of curvature is adjusted to generate improved tooth profile geometric parameters, which are used to optimize meshing performance.

9. A wear prediction system for a crane transmission system, used to implement the method as described in any one of claims 1-8, characterized in that, The system includes: The first acquisition unit is used to obtain the tooth profile geometric parameters and material fatigue characteristics from the gear design parameters, determine the meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtain the contact point displacement sequence. The determining unit is used to extract the trajectory node distribution and calculate the curvature distribution based on the contact point displacement sequence, and to determine the contact point migration rate and velocity gradient distribution based on the curvature distribution; The calculation unit is used to determine the rate of change of the directional angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and calculate the contact pressure distribution at the abrupt change point using Hertzian contact theory. The second acquisition unit is used to determine the location of stress concentration points based on the contact pressure distribution at the abrupt change point, calculate the local wear rate using the wear rate calculation formula, and acquire local wear distribution data of the tooth surface. The optimization unit is used to obtain the high wear area based on the wear distribution data, analyze the stress concentration point distribution of the high wear area through dynamic finite element simulation, adjust the radius of curvature to generate improved tooth profile geometric parameters, recalculate the optimized contact point displacement sequence and local wear distribution data, and obtain the contact point distribution optimization result.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the method as described in any one of claims 1-8.

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